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3 <page xmlns="http://lambdadelta.info/"
4 description = "\lambda\delta home page"
5 title = "\lambda\delta home page"
7 head = "The Formal Systems of the λδ (\lambda\delta) Family"
9 <sitemap name="sitemap"/>
11 <section9 name="foreword">Foreword</section9>
13 The formal systems of the λδ (\lambda\delta) family are typed λ-calculi aiming to support
14 the foundational frameworks for Mathematics that require an underlying specification language,
16 <link to="http://www.math.unipd.it/~maietti/">Minimalist Foundation (MF)</link>
20 The λδ family is developed within the
21 <link to="http://helm.cs.unibo.it/">Hypertextual Electronic Library of Mathematics (HELM)</link>
22 as a set of machine-checked <rlink to="html/specification.html">digital specifications</rlink>.
24 <topitem name="current">
26 <notice class="alpha" text="The current specification: "/>
27 <rlink to="download/lambdadelta_2B.tar.bz2">λδ-2B for for Matita 0.99.4</rlink>
28 (revised: <notice class="gamma" notice="2020-12"/>).
29 <rlink to="html/documentation.html#ldJ2a">Documentation (J2a)</rlink>.
32 <notice class="alpha" text="The current specification depends on: "/>
33 <rlink to="download/lambdadelta_ground.tar.bz2">λδ-ground for Matita 0.99.2</rlink>
34 (revised <notice class="gamma" text="2020-12"/>).
38 This is the family logo: <rlink to="images/crux_177.png">crux_177.png</rlink>
39 (revised <notice class="alpha" text="2012-09"/>).
42 <notice class="alpha" text="Notice:"/>
43 to view this site correctly, please install fonts
44 supporting <link to="http://www.unicode.org/">Unicode 7.0</link> (June 2014).
45 For instance <notice class="alpha" text="Unifont Upper"/>
46 or <notice class="alpha" text="Symbola"/>
47 or <notice class="alpha" text="Noto Sans Symbols2"/>.
50 <ucs-bronze char="03BB"/>
51 <ucs-bronze char="03C7"/>
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57 <section9 name="citations">Citations</section9>
59 This is a list of publications citing λδ documentation.
63 Yaoshun Fu, Wensheng Yu:
64 <notice class="alpha">Formalizing Calculus without Limit Theory in Coq</notice>
65 (2021). In Mathematics, 9(12), pp. 1377:1-1377:24.
70 <notice class="alpha">An extended type system with lambda-typed lambda-expressions</notice>
71 (2020). In Logical Methods in Computer Science, 16(4), pp. 12:1-12:50.
76 <notice class="alpha">An extended type system with lambda-typed lambda-expressions (extended version)</notice>
77 (2020). Technical report. Faculty of Computer Science, Technical University of Berlin.
81 M.E. Maietti, S. Maschio:
82 <notice class="alpha">An extensional Kleene realizability semantics for the Minimalist Foundation</notice>
83 (2015). In Leibniz International Proceedings in Informatics, 39, pp 162-186. Schloss Dagstuhl, Leibniz-Zentrum für Informatik.
87 C. Dunchev, F. Guidi, C. Sacerdoti Coen, E. Tassi:
88 <notice class="alpha">ELPI: Fast, Embeddable, λProlog Interpreter</notice>
89 (2015). In proc. of LPAR 20. Lecture Notes in Computer Science, 9450, pp. 460-468. Springer.
93 A. Asperti, W. Ricciotti, C. Sacerdoti Coen, E. Tassi:
94 <notice class="alpha">Formal metatheory of programming languages in the Matita interactive theorem prover</notice>
95 (2012). In Journal of Automated Reasoning, 49(3), pp. 427-451. Springer.
100 <notice class="alpha">Consistency of the minimalist foundation with Church thesis and Bar Induction</notice>
101 (2012). Submitted article.
106 <notice class="alpha">Theoretical and implementation aspects in the mechanization of the metatheory of programming languages</notice>
107 (July 2011). Ph.D. Thesis in Computer Science, Technical Report UBLCS-2011-09, University of Bologna.
112 <notice class="alpha">Faithful Reproductions of the Automath Landau Formalization</notice>
113 (2011). Technical report.
118 <notice class="alpha">A minimalist two-level foundation for constructive mathematics</notice>
119 (2009). In Annals of Pure and Applied Logic, 160(3), pp. 319-354. Elsevier.
124 <notice class="alpha">First Year Report: Realisability methods of proof and semantics with application to expansion</notice>
125 (July 2007). Technical report.
128 <!-- ===================================================================== -->
130 <section9 name="disclaimer">Disclaimer</section9>
132 The systems of the λδ family <notice class="alpha" text="are not"/> related intentionally to
133 any other system having (variations of) the symbols λ and δ in its name or syntax.
134 Examples include (but are not limited to):
138 <notice class="alpha">λ-δ</notice> of
140 <notice class="alpha">The calculi of lambda-conversion</notice>
142 Annals of Mathematics Studies 6.
143 Princeton University Press.
147 <notice class="alpha">∆Λ</notice> of
149 <notice class="alpha">Generalizing Automath by means of a lambda-typed lambda calculus</notice>
151 In Lecture Notes in Pure and Applied Mathematics 106, pp. 71-92.
156 <notice class="alpha">λ<sub>∆</sub></notice> of
157 N.J. Rehof, M.H. Sørensen:
158 <notice class="alpha">The λ<sub>∆</sub>-calculus</notice>
160 In Lecture Notes in Computer Science, 789, pp. 516–542.
165 <notice class="alpha">λ∆</notice> of
166 S. Ronchi Della Rocca, L. Paolini:
167 <notice class="alpha">The Parametric Lambda Calculus</notice>
169 Texts in Theoretical Computer Science, An EATCS Series.
174 <notice class="alpha">λD</notice> of
175 R. Nederpelt, H. Geuvers:
176 <notice class="alpha">Type Theory and Formal Proof</notice>
178 Cambridge University Press.
182 <notice class="alpha">Cλξ</notice> of
184 <notice class="alpha">A namefree lambda calculus with facilities for internal definition of expressions and segments</notice>
187 Eindhoven University of Technology, Eindhoven.
192 Moreover, the systems of the λδ family <notice class="alpha" text="are not"/> related intentionally to
193 <link to="http://umineko.wikia.com/wiki/Lambdadelta">Lady Lambdadelta</link>,
194 the Witch of Certainty of the sound novel
195 <link to="https://it.wikipedia.org/wiki/Umineko_no_naku_koro_ni">Umineko no Naku Koro ni</link>.
198 <!-- ===================================================================== -->
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